What type of function is an inverse function and what happens to the domain of the function when it's inverse is taken?
Inverse function is a one to one function. The graph of an inverse function is the reflection of the original graph over the identity line of y = x. Sometimes it may be necessary to restrict the domain to make sure the inverse is a function.
A certain gas initially at 0.050 L undergoes expansion until its volume is 0.50 L. Calculate the work done (in joules) by the gas if it expands against a vacuum.
0 Joules is the answer. Since the pressure in vacuum is zero, there is no work done by the gas.
What is the derivative of (5x)^e where is e is the constant 2.718?
1. Set up the equation. y= (5x)^e 2. Take the derivative. dy/dx= d/dx ((5x)^e) dy/dx=y'=d/dx ((5x)^e) (y prime is the same as dy/dx) (This step is optional. The equation can be kept in terms of dy/dx) y'=d/dx ((5x)^e) (re-write the equation without dy/dx) (This step is optional. The equation can be kept in terms of dy/dx) y'=d/dx (5^e * x^e) (distribute the exponent of 'e' to '5' and 'x') y'=5^e d/dx (x^e) (Since 5^e is a constant, it can be brought outside the derivative operator) y'=(5^e) (e * x^(e-1)) (Do the product rule for x^e ) y'=e5^e * x^(e-1) (Final Answer)